Information on Result #1013826
Linear OOA(7110, 7686412, F7, 3, 10) (dual of [(7686412, 3), 23059126, 11]-NRT-code), using (u, u+v)-construction based on
- linear OOA(734, 5764804, F7, 3, 5) (dual of [(5764804, 3), 17294378, 6]-NRT-code), using
- trace code [i] based on linear OOA(4917, 2882402, F49, 3, 5) (dual of [(2882402, 3), 8647189, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(4917, 5764805, F49, 5) (dual of [5764805, 5764788, 6]-code), using
- construction X applied to Ce(4) ⊂ Ce(3) [i] based on
- linear OA(4917, 5764801, F49, 5) (dual of [5764801, 5764784, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 494−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(4913, 5764801, F49, 4) (dual of [5764801, 5764788, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 494−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(490, 4, F49, 0) (dual of [4, 4, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(490, s, F49, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(4) ⊂ Ce(3) [i] based on
- OOA 2-folding and stacking with additional row [i] based on linear OA(4917, 5764805, F49, 5) (dual of [5764805, 5764788, 6]-code), using
- trace code [i] based on linear OOA(4917, 2882402, F49, 3, 5) (dual of [(2882402, 3), 8647189, 6]-NRT-code), using
- linear OOA(776, 3843206, F7, 3, 10) (dual of [(3843206, 3), 11529542, 11]-NRT-code), using
- trace code [i] based on linear OOA(4938, 1921603, F49, 3, 10) (dual of [(1921603, 3), 5764771, 11]-NRT-code), using
- OOA 3-folding [i] based on linear OA(4938, 5764809, F49, 10) (dual of [5764809, 5764771, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(4938, 5764810, F49, 10) (dual of [5764810, 5764772, 11]-code), using
- construction X applied to Ce(9) ⊂ Ce(7) [i] based on
- linear OA(4937, 5764801, F49, 10) (dual of [5764801, 5764764, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 494−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(4929, 5764801, F49, 8) (dual of [5764801, 5764772, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 494−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(491, 9, F49, 1) (dual of [9, 8, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(491, s, F49, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to Ce(9) ⊂ Ce(7) [i] based on
- discarding factors / shortening the dual code based on linear OA(4938, 5764810, F49, 10) (dual of [5764810, 5764772, 11]-code), using
- OOA 3-folding [i] based on linear OA(4938, 5764809, F49, 10) (dual of [5764809, 5764771, 11]-code), using
- trace code [i] based on linear OOA(4938, 1921603, F49, 3, 10) (dual of [(1921603, 3), 5764771, 11]-NRT-code), using
Mode: Constructive and linear.
Optimality
Show details for fixed k and m, k and s, k and t, m and s, m and t.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OOA(7110, 3843205, F7, 15, 10) (dual of [(3843205, 15), 57647965, 11]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |